FIA NLS Models: Biomass vs. Stand Age, G-Reconciled
JAH
2022-12-14
Background
This document has nls (non-linear least squares) regression fits to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass vs. stand age relationships. We calculated the biomass of each FIA plot by summing alive tree biomass (as reported by FIA). Stand age is also reported by FIA, using tree-core age estimates from two trees from the dominant size class of the FIA plot.
We considered the following Michaelis-Menten functional form \(B = (1 + (yr-1990)* ge/100) \times (1 - \alpha \cdot B_l) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac{A \cdot STDAGE_{t2}}{k+STDAGE_{t2}}\right)\), where \(B\) is the plot biomass, \(B_l\) is the calculated biomass loss (proportion) for the previous FIA plot census interval, \(STDAGE_{t2}\) is the stand age at the second of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the peak growing season (June-August) annual average PDSI values over the FIA plot measurement intervals and a 30-year climate normal (1960-1989), and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(ge\): biomass growth enhancement over time, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.
Data have increasing variance in \(B\) with increasing \(STDAGE_{t2}\), thus, weighted-nls is the best approach. We explored a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {meanG}^2\) in equal-sample sized stand age bins (n=20 where possible, else n=10) for each ecoprovince. These bins are also used to visualize data means in relation to nls model fit.
Model selection is used to determine the best fitting models, which is implemented in three parts. The first part selected the best model form using \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest) and \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or the difference in the Palmer drought severity index from June - August for the 10 years preceding the biomass measurement and the 1960-1989 period).
model 1: simple model \(B = (1 + (yr-1990)* ge/100) \times \left( \frac {A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)
model 2: phi model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)
model 3: phi-alpha model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)
Then, model selection part two takes the best fitting model from part 1 and and adds the \(p\) and \(s\) parameters (individually then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.
sub-model a: p form \(pA + \left( \frac {(1-p) * A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)
sub-model b: s form \(\left( \frac {A \cdot STDAGE_{t2}^s} {k^s+STDAGE_{t2}^s} \right)\)
sub-model c: p and s together \(pA + \left( \frac {(1-p) *A \cdot STDAGE_{t2}^s} {k^s + STDAGE_{t1}^s} \right)\)
Lastly, model selection part 3, fits three similar models to model selection part one, but uses the Log-Normal functional form. The Log-Normal equation fits more of “hump-shaped” curve which allows for a decrease in biomass at old stand ages. Three Log-normal models are fitted: 1) the simple model, 2) the \(\phi\) model: accounting for climate variability (i.e., \(\Delta PDSI\)) and 3: the \(\phi\)-\(\alpha\) model: account for both climate variability and growth compensation due to plot biomass loss.
model 4: simple model \(B = (1 + (yr-1990)* ge/100) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(STDAGE_{t2} /c \right)} {d} \right]} ^2 \right)\)
model 5: phi model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(STDAGE_{t2} /c \right)} {d} \right]} ^2 \right)\)
model 6: phi-alpha model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(STDAGE_{t2} /c \right)} {d} \right]} ^2 \right)\)
Note:
This analysis only uses plot biomass data from the same plot locations and measurement intervals for which we also have data on biomass growth (which is used in the growth vs. biomass analysis ). We use the second of the two plot measurements comprising a \(G\) interval
This includes the following plot-based filtering criteria (which were used for the growth vs. biomass analysis):
- exclude FIA plots in plantation forests
- exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
- exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
- exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
- exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
- exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)
Below the model fitting procedure is implemented by ecoprovince:
211 - Northeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6880 1758.3
## 2 6879 1757.8 1 0.555 2.1712 0.1407
## 3 6826 1549.2 53 208.623 17.3444 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 74579.98
## 2 2 74579.81
## 3 3 73288.96##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.783844 0.191166 4.100 4.17e-05 ***
## phi -0.006083 0.004050 -1.502 0.133
## alpha 0.848174 0.027710 30.609 < 2e-16 ***
## A 387.282360 24.219054 15.991 < 2e-16 ***
## k 170.939329 11.561396 14.785 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4764 on 6826 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 3.994e-06
## (53 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in Mod.Sel3 %in% c(1, "1a", "1b", "1c", 4) :
## object 'Mod.Sel3' not found
## Error in Mod.Sel3 %in% c(1, "1a", "1b", "1c", 4) :
## object 'Mod.Sel3' not found
## Error in Mod.Sel3 %in% c(1, "1a", "1b", "1c", 4) :
## object 'Mod.Sel3' not found
## model AIC
## 1 3 73288.96
## 2 3a NA
## 3 3b NA
## 4 3c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.783844 0.191166 4.100 4.17e-05 ***
## phi -0.006083 0.004050 -1.502 0.133
## alpha 0.848174 0.027710 30.609 < 2e-16 ***
## A 387.282360 24.219054 15.991 < 2e-16 ***
## k 170.939329 11.561396 14.785 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4764 on 6826 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 3.994e-06
## (53 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6878 1726.3
## 2 6877 1726.3 1 0.00 0.000 0.9999
## 3 6824 1505.9 53 220.44 18.849 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 73288.96
## 2 4 74457.48
## 3 5 74459.48
## 4 6 73099.37##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 8.813e-01 1.963e-01 4.489 7.27e-06 ***
## phi 0.000e+00 4.073e-03 0.000 1
## alpha 8.427e-01 2.665e-02 31.622 < 2e-16 ***
## a 3.796e+01 1.716e+00 22.121 < 2e-16 ***
## b 1.029e+02 4.675e+00 22.003 < 2e-16 ***
## c 1.147e+02 4.219e+00 27.183 < 2e-16 ***
## d 9.253e-01 3.938e-02 23.497 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4698 on 6824 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (53 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: fits
plot residuals
predict and plot
plotting 2
212 - Laurentian Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 22648 8866.6
## 2 22642 8863.1 6 3.45 1.4684 0.1846
## 3 18851 6790.9 3791 2072.26 1.5174 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 236627.9
## 2 2 236569.9
## 3 3 196512.3##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.912e-01 1.133e-01 2.570 0.01017 *
## phi 7.851e-03 2.877e-03 2.729 0.00637 **
## alpha 7.062e-01 2.262e-02 31.215 < 2e-16 ***
## A 1.736e+02 4.978e+00 34.871 < 2e-16 ***
## k 6.414e+01 1.924e+00 33.330 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6002 on 18851 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 5.698e-07
## (3829 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 18851 6790.9
## 2 18850 6692.5 1 98.406 277.17 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 196512.3
## 2 3a 196239.1
## 3 3b 196471.9
## 4 3c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.241e-01 1.093e-01 2.050 0.04040 *
## phi 9.052e-03 2.859e-03 3.166 0.00155 **
## alpha 7.201e-01 1.902e-02 37.853 < 2e-16 ***
## A 2.301e+02 1.078e+01 21.336 < 2e-16 ***
## k 1.220e+02 8.649e+00 14.107 < 2e-16 ***
## p 4.587e-02 2.123e-03 21.611 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5959 on 18850 degrees of freedom
##
## Number of iterations to convergence: 14
## Achieved convergence tolerance: 7.141e-06
## (3829 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 22646 8719.0
## 2 22640 8716.1 6 2.81 1.2177 0.2935
## 3 18849 6477.4 3791 2238.72 1.7184 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3a 196239.1
## 2 4 236251.5
## 3 5 236195.2
## 4 6 195625.2##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 4.140e-01 1.162e-01 3.563 0.000368 ***
## phi 7.961e-03 2.783e-03 2.860 0.004237 **
## alpha 7.834e-01 1.478e-02 52.994 < 2e-16 ***
## a 2.394e+01 6.952e-01 34.428 < 2e-16 ***
## b 8.032e+01 2.177e+00 36.900 < 2e-16 ***
## c 1.097e+02 2.987e+00 36.713 < 2e-16 ***
## d 1.196e+00 2.919e-02 40.962 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5862 on 18849 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (3829 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: fits
plot residuals
predict and plot
plotting 2
221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7303 1344.5
## 2 7302 1344.5 1 0.043 0.2328 0.6295
## 3 7236 1180.4 66 164.021 15.2340 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 79950.98
## 2 2 79952.75
## 3 3 78504.02##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.150534 0.121581 1.238 0.216
## phi -0.002307 0.003371 -0.684 0.494
## alpha 0.820917 0.026455 31.031 <2e-16 ***
## A 488.035490 25.376755 19.232 <2e-16 ***
## k 148.175964 8.787433 16.862 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4039 on 7236 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.121e-06
## (66 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7236 1180.4
## 2 7235 1180.4 1 0.072623 0.4451 0.5047
## model AIC
## 1 3 78504.02
## 2 3a 78505.57
## 3 3b 78486.11
## 4 3c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s +
## STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.199221 0.124547 1.600 0.110
## phi -0.002882 0.003363 -0.857 0.392
## alpha 0.828632 0.026693 31.043 <2e-16 ***
## A 328.159568 25.015982 13.118 <2e-16 ***
## k 75.605699 8.503967 8.891 <2e-16 ***
## s 1.204149 0.047079 25.577 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4034 on 7235 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 1.269e-06
## (66 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7301 1330.8
## 2 7300 1330.8 1 0.00 0.000 1
## 3 7234 1163.2 66 167.61 15.794 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3b 78486.11
## 2 4 79879.95
## 3 5 79881.95
## 4 6 78401.23##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.821e-01 1.229e-01 1.482 0.138
## phi 0.000e+00 3.355e-03 0.000 1.000
## alpha 8.235e-01 2.507e-02 32.842 <2e-16 ***
## a 3.031e+01 2.059e+00 14.722 <2e-16 ***
## b 1.653e+02 7.505e+00 22.022 <2e-16 ***
## c 1.365e+02 9.187e+00 14.864 <2e-16 ***
## d 1.344e+00 6.315e-02 21.287 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.401 on 7234 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (66 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: fits
plot residuals
predict and plot
plotting 2
222 - Midwest Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5841 1995.4
## 2 5840 1991.5 1 3.94 11.5553 0.0006801 ***
## 3 4837 1493.8 1003 497.67 1.6066 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## model AIC
## 1 1 62741.48
## 2 2 62731.93
## 3 3 51869.23##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.198275 0.190865 -1.039 0.298940
## phi 0.026927 0.008166 3.298 0.000982 ***
## alpha 0.840626 0.041923 20.052 < 2e-16 ***
## A 433.451485 35.586083 12.180 < 2e-16 ***
## k 179.023537 16.475977 10.866 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5557 on 4837 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 5.237e-06
## (1004 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4837 1493.8
## 2 4836 1493.8 1 0.065605 0.2124 0.6449
## model AIC
## 1 3 51869.23
## 2 3a 51871.01
## 3 3b 51851.13
## 4 3c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s +
## STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.142003 0.196013 -0.724 0.468819
## phi 0.026869 0.008145 3.299 0.000978 ***
## alpha 0.861714 0.042348 20.348 < 2e-16 ***
## A 254.478620 25.639783 9.925 < 2e-16 ***
## k 74.310141 10.351858 7.178 8.12e-13 ***
## s 1.259046 0.060453 20.827 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5546 on 4836 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 4.249e-06
## (1004 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5839 1955.8
## 2 5838 1951.5 1 4.28 12.8130 0.000347 ***
## 3 4835 1439.8 1003 511.71 1.7132 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3b 51851.13
## 2 4 62628.31
## 3 5 62617.50
## 4 6 51694.96##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.160480 0.191030 -0.840 0.400905
## phi 0.029310 0.008058 3.637 0.000279 ***
## alpha 0.861198 0.034858 24.706 < 2e-16 ***
## a 26.981910 1.590173 16.968 < 2e-16 ***
## b 117.431325 5.506609 21.326 < 2e-16 ***
## c 102.339914 4.395032 23.285 < 2e-16 ***
## d 1.016947 0.045310 22.444 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5457 on 4835 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1004 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: fits
plot residuals
predict and plot
plotting 2
223 - Central Interior Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 9996 1894.8
## 2 9995 1886.1 1 8.62 45.6873 1.465e-11 ***
## 3 8720 1565.2 1275 320.92 1.4023 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 104296.40
## 2 2 104252.80
## 3 3 90827.83##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.396833 0.125814 3.154 0.00162 **
## phi -0.024935 0.004067 -6.130 9.15e-10 ***
## alpha 0.760649 0.027047 28.124 < 2e-16 ***
## A 238.294969 8.772491 27.164 < 2e-16 ***
## k 71.732427 3.342762 21.459 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4237 on 8720 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 6.33e-06
## (1281 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8720 1565.2
## 2 8719 1565.0 1 0.16787 0.9352 0.3335
## model AIC
## 1 3 90827.83
## 2 3a 90828.90
## 3 3b 90795.04
## 4 3c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s +
## STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.416271 0.126666 3.286 0.00102 **
## phi -0.024882 0.004055 -6.136 8.81e-10 ***
## alpha 0.766041 0.027202 28.161 < 2e-16 ***
## A 173.765420 8.048890 21.589 < 2e-16 ***
## k 40.143985 2.546281 15.766 < 2e-16 ***
## s 1.357396 0.059895 22.663 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4229 on 8719 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.878e-06
## (1281 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 9994 1868.9
## 2 9993 1868.9 1 0.00 0.0000 1
## 3 8718 1536.5 1275 332.39 1.4792 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3b 90795.04
## 2 4 104162.96
## 3 5 104164.96
## 4 6 90670.25##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.11966 0.11180 1.07 0.285
## phi 0.00000 0.00420 0.00 1.000
## alpha 0.76968 0.02606 29.54 <2e-16 ***
## a 31.40349 1.94921 16.11 <2e-16 ***
## b 103.16963 3.49693 29.50 <2e-16 ***
## c 102.24775 4.00727 25.52 <2e-16 ***
## d 1.21270 0.05205 23.30 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4198 on 8718 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1281 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: fits
plot residuals
predict and plot
plotting 2
231 - Southeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12796 4809.1
## 2 12795 4808.7 1 0.36 0.9571 0.3279
## 3 12521 4175.2 274 633.57 6.9343 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 141420.6
## 2 2 141421.7
## 3 3 137622.5##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.298741 0.153046 8.486 <2e-16 ***
## phi -0.004157 0.003895 -1.067 0.286
## alpha 0.589610 0.018270 32.273 <2e-16 ***
## A 218.121169 7.367848 29.604 <2e-16 ***
## k 49.029679 1.573432 31.161 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5775 on 12521 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 4.048e-06
## (318 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_231, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12521 4175.2
## 2 12520 3964.7 1 210.43 664.52 < 2.2e-16 ***
## 3 12519 3859.6 1 105.14 341.03 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 137622.5
## 2 3a 136976.7
## 3 3b NA
## 4 3c 136642.1##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.217572 0.194135 11.423 <2e-16 ***
## phi -0.004290 0.003665 -1.171 0.242
## alpha 0.806123 0.010262 78.552 <2e-16 ***
## A 126.582471 4.627536 27.354 <2e-16 ***
## k 32.083156 0.874214 36.699 <2e-16 ***
## p 0.201159 0.007276 27.645 <2e-16 ***
## s 2.406768 0.105540 22.804 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5552 on 12519 degrees of freedom
##
## Number of iterations to convergence: 16
## Achieved convergence tolerance: 8.359e-06
## (318 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12794 4770.2
## 2 12793 4770.2 1 0.0 0.000 0.9999
## 3 12519 3858.0 274 912.2 10.803 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3c 136642.1
## 2 4 141320.7
## 3 5 141322.7
## 4 6 136636.9##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.122e+00 1.886e-01 11.25 <2e-16 ***
## phi 0.000e+00 3.654e-03 0.00 1
## alpha 8.066e-01 1.021e-02 79.00 <2e-16 ***
## a 2.610e+01 7.952e-01 32.82 <2e-16 ***
## b 9.784e+01 3.899e+00 25.10 <2e-16 ***
## c 1.017e+02 5.567e+00 18.27 <2e-16 ***
## d 1.383e+00 4.701e-02 29.43 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5551 on 12519 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (318 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: fits
plot residuals
predict and plot
plotting 2
232 - Outer Coastal Plain Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13052 7462.8
## 2 13051 7457.1 1 5.67 9.9174 0.001641 **
## 3 12737 6769.2 314 687.93 4.1223 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 146999.4
## 2 2 146991.5
## 3 3 143242.9##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 8.326e-01 1.651e-01 5.042 4.67e-07 ***
## phi 1.285e-02 4.608e-03 2.789 0.0053 **
## alpha 6.349e-01 1.913e-02 33.183 < 2e-16 ***
## A 2.157e+02 8.767e+00 24.605 < 2e-16 ***
## k 4.550e+01 1.798e+00 25.310 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.729 on 12737 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 2.205e-06
## (425 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_232, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_232, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12737 6769.2
## 2 12736 6281.7 1 487.49 988.38 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 143242.9
## 2 3a 142292.6
## 3 3b NA
## 4 3c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.282e+00 1.808e-01 7.093 1.38e-12 ***
## phi 2.125e-02 4.315e-03 4.924 8.59e-07 ***
## alpha 8.382e-01 9.762e-03 85.865 < 2e-16 ***
## A 6.850e+02 1.294e+02 5.296 1.20e-07 ***
## k 3.849e+02 8.839e+01 4.354 1.34e-05 ***
## p 3.517e-02 5.927e-03 5.935 3.01e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7023 on 12736 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 8.658e-06
## (425 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13050 7396.2
## 2 13049 7390.0 1 6.16 10.8706 0.0009796 ***
## 3 12735 6114.6 314 1275.39 8.4595 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3a 142292.6
## 2 4 146886.4
## 3 5 146877.5
## 4 6 141951.1##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.323e+00 1.792e-01 7.379 1.69e-13 ***
## phi 2.238e-02 4.214e-03 5.312 1.10e-07 ***
## alpha 8.716e-01 8.279e-03 105.282 < 2e-16 ***
## a 3.279e+01 1.074e+00 30.514 < 2e-16 ***
## b 1.046e+02 4.797e+00 21.803 < 2e-16 ***
## c 1.062e+02 6.936e+00 15.316 < 2e-16 ***
## d 1.323e+00 5.441e-02 24.316 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6929 on 12735 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (425 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: fits
plot residuals
predict and plot
plotting 2
234 - Lower Mississippi Riverine Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1339 479.03
## 2 1338 477.61 1 1.417 3.9708 0.0465 *
## 3 1277 328.24 61 149.369 9.5264 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 15098.92
## 2 2 15096.94
## 3 3 14148.33##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.05537 0.41382 0.134 0.894
## phi 0.02170 0.01451 1.496 0.135
## alpha 0.66209 0.05415 12.226 < 2e-16 ***
## A 550.84136 93.74731 5.876 5.36e-09 ***
## k 164.62568 31.36459 5.249 1.79e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.507 on 1277 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.843e-06
## (62 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_234, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1277 328.24
## 2 1276 328.19 1 0.044987 0.1749 0.6759
## model AIC
## 1 3 14148.33
## 2 3a 14150.15
## 3 3b 14149.70
## 4 3c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.05537 0.41382 0.134 0.894
## phi 0.02170 0.01451 1.496 0.135
## alpha 0.66209 0.05415 12.226 < 2e-16 ***
## A 550.84136 93.74731 5.876 5.36e-09 ***
## k 164.62568 31.36459 5.249 1.79e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.507 on 1277 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.843e-06
## (62 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Error in nls(f_5, data = G_234, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: singular convergence (7)
## Error in nls(f_6, data = G_234, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: iteration limit reached without convergence (10)
## model AIC
## 1 3 14148.33
## 2 4 15100.79
## 3 5 NA
## 4 6 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.05537 0.41382 0.134 0.894
## phi 0.02170 0.01451 1.496 0.135
## alpha 0.66209 0.05415 12.226 < 2e-16 ***
## A 550.84136 93.74731 5.876 5.36e-09 ***
## k 164.62568 31.36459 5.249 1.79e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.507 on 1277 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.843e-06
## (62 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: does not fit
- log-normal phi-alpha model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.95697, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -11.379, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
242 - Pacific Lowland Mixed Forest
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
- log-normal phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"251 - Prairie Parkland (Temperate)
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2284 617.34
## 2 2283 617.31 1 0.034 0.1246 0.7241
## 3 1779 393.26 504 224.054 2.0110 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 24037.04
## 2 2 24038.91
## 3 3 18554.02##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.452101 0.337258 1.341 0.180
## phi -0.009728 0.008348 -1.165 0.244
## alpha 0.723061 0.066976 10.796 <2e-16 ***
## A 253.307381 25.881776 9.787 <2e-16 ***
## k 100.370377 11.700089 8.579 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4702 on 1779 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 2.02e-06
## (506 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1779 393.26
## 2 1778 393.16 1 0.099492 0.4499 0.5025
## model AIC
## 1 3 18554.02
## 2 3a 18555.57
## 3 3b 18535.55
## 4 3c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s +
## STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.461374 0.337089 1.369 0.171
## phi -0.007587 0.008354 -0.908 0.364
## alpha 0.734801 0.067811 10.836 <2e-16 ***
## A 145.037642 13.621784 10.647 <2e-16 ***
## k 38.922297 3.519170 11.060 <2e-16 ***
## s 1.702253 0.153066 11.121 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4676 on 1778 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 9.034e-06
## (506 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2282 595.32
## 2 2281 595.32 1 0.00 0.0000 1
## 3 1777 380.67 504 214.65 1.9881 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3b 18535.55
## 2 4 23957.97
## 3 5 23959.97
## 4 6 18500.01##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.316611 0.315076 1.005 0.315
## phi 0.000000 0.008366 0.000 1.000
## alpha 0.721003 0.065836 10.952 < 2e-16 ***
## a 26.749847 3.883232 6.889 7.8e-12 ***
## b 93.309963 7.589862 12.294 < 2e-16 ***
## c 99.589633 6.919253 14.393 < 2e-16 ***
## d 1.097516 0.093714 11.711 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4628 on 1777 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (506 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.9672, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -18.437, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
255 - Prairie Parkland (Subtropical)
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 708 336.70
## 2 707 336.59 1 0.114 0.2387 0.6253
## 3 663 256.40 44 80.193 4.7129 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 7311.058
## 2 2 7312.818
## 3 3 6847.424##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.11049 0.45757 -0.241 0.809
## phi -0.01619 0.01548 -1.046 0.296
## alpha 0.58972 0.09275 6.358 3.81e-10 ***
## A 194.05332 30.30528 6.403 2.88e-10 ***
## k 60.73530 10.48651 5.792 1.08e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6219 on 663 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 5.75e-06
## (46 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 663 256.4
## 2 662 253.4 1 2.9955 7.8256 0.005301 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 6847.424
## 2 3a 6841.574
## 3 3b 6848.960
## 4 3c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.015226 0.475959 -0.032 0.97449
## phi -0.015314 0.015369 -0.996 0.31943
## alpha 0.598558 0.086108 6.951 8.69e-12 ***
## A 266.510967 86.162862 3.093 0.00206 **
## k 119.972028 58.508932 2.050 0.04071 *
## p 0.032368 0.008238 3.929 9.42e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6187 on 662 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 9.122e-06
## (46 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 706 321.06
## 2 705 320.94 1 0.124 0.2721 0.6021
## 3 661 239.34 44 81.603 5.1221 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3a 6841.574
## 2 4 7281.242
## 3 5 7282.967
## 4 6 6805.432##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.18595 0.42015 -0.443 0.658
## phi 0.00000 0.01468 0.000 1.000
## alpha 0.64304 0.07775 8.271 7.33e-16 ***
## a 22.55849 2.85029 7.914 1.05e-14 ***
## b 75.97870 8.55425 8.882 < 2e-16 ***
## c 59.50946 5.45495 10.909 < 2e-16 ***
## d 0.99855 0.11455 8.717 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6017 on 661 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (46 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93637, p-value = 2.822e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -9.5618, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
261 - California Coastal Chaparral Forest and Shrub
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
add p model: does not fit
add s model: does not fit
add s+p model: does not fit
unable to fit model (only 64 observations)
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
- log-normal phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"262 - California Dry Steppe
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
add p model: does not fit
add s model: does not fit
add s+p model: does not fit
unable to fit model (0 observations)
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
- log-normal phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"263 - California Coastal Steppe - Mixed Forest and Redwood Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 155 28.883
## 2 154 28.876 1 0.00774 0.0413 0.83924
## 3 150 26.624 4 2.25207 3.1721 0.01552 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 1995.769
## 2 2 1997.727
## 3 3 1954.695##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.20199 1.19725 -0.169 0.86625
## phi -0.05404 0.06721 -0.804 0.42264
## alpha 0.75695 0.24731 3.061 0.00262 **
## A 6638.54989 2801.18595 2.370 0.01906 *
## k 1264.32167 414.66988 3.049 0.00271 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4213 on 150 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 6.736e-06
## (4 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_263, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_263, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 150 26.624
## 2 149 25.750 1 0.87387 5.0566 0.026 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 1954.695
## 2 3a 1951.522
## 3 3b NA
## 4 3c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -7.777e-02 1.282e+00 -0.061 0.951698
## phi -2.712e-02 6.706e-02 -0.404 0.686456
## alpha 8.593e-01 2.401e-01 3.579 0.000466 ***
## A 1.932e+04 2.056e+04 0.940 0.348869
## k 4.916e+03 5.597e+03 0.878 0.381211
## p 3.006e-03 2.553e-03 1.178 0.240857
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4157 on 149 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 5.081e-06
## (4 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 153 30.979
## 2 152 30.979 1 0.0000 0.0000 1.00000
## 3 148 28.736 4 2.2433 2.8885 0.02441 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3a 1951.522
## 2 4 2010.835
## 3 5 2012.835
## 4 6 1970.528##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -7.777e-02 1.282e+00 -0.061 0.951698
## phi -2.712e-02 6.706e-02 -0.404 0.686456
## alpha 8.593e-01 2.401e-01 3.579 0.000466 ***
## A 1.932e+04 2.056e+04 0.940 0.348869
## k 4.916e+03 5.597e+03 0.878 0.381211
## p 3.006e-03 2.553e-03 1.178 0.240857
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4157 on 149 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 5.081e-06
## (4 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94451, p-value = 8.565e-06
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -2.165, p-value = 0.03038
## alternative hypothesis: two.sidedpredict and plot
plotting 2
313 - Colorado Plateau Semi-Desert
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 214 67.657
## 2 213 67.601 1 0.05588 0.1761 0.6752
## 3 210 67.034 3 0.56784 0.5930 0.6203
## model AIC
## 1 1 2322.942
## 2 2 2324.763
## 3 3 2310.678##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.75338 0.99763 -0.755 0.4510
## phi 0.01946 0.03797 0.512 0.6089
## alpha -0.08479 0.30668 -0.276 0.7825
## A 258.05809 102.79459 2.510 0.0128 *
## k 135.22109 55.86986 2.420 0.0164 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.565 on 210 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 5.081e-06
## (3 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 210 67.034
## 2 209 67.029 1 0.0047244 0.0147 0.9035
## model AIC
## 1 3 2310.678
## 2 3a 2312.663
## 3 3b 2311.948
## 4 3c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.75338 0.99763 -0.755 0.4510
## phi 0.01946 0.03797 0.512 0.6089
## alpha -0.08479 0.30668 -0.276 0.7825
## A 258.05809 102.79459 2.510 0.0128 *
## k 135.22109 55.86986 2.420 0.0164 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.565 on 210 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 5.081e-06
## (3 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 212 62.692
## 2 211 62.495 1 0.19729 0.6661 0.4153
## 3 208 60.709 3 1.78543 2.0391 0.1095
## model AIC
## 1 3 2310.678
## 2 4 2310.402
## 3 5 2311.718
## 4 6 2293.372##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.28713 0.67518 -1.906 0.057982 .
## phi 0.03227 0.03517 0.918 0.359882
## alpha 0.29974 0.24631 1.217 0.225013
## a 53.32207 16.30891 3.270 0.001261 **
## b 144.62680 42.16073 3.430 0.000727 ***
## c 139.92344 7.50050 18.655 < 2e-16 ***
## d 0.57294 0.08596 6.665 2.33e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5403 on 208 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (3 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.91535, p-value = 9.76e-10
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -1.201, p-value = 0.2297
## alternative hypothesis: two.sidedpredict and plot
plotting 2
315 - Southwest Plateau and Plains Dry Steppe and Shrub
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
- log-normal phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"321 - Chihuahuan Semi-Desert
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
- log-normal phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"322 - American Semidesert and Desert
model selection 1
## Error in nls(f_1, data = G_322, start = c(ge = ge.start, A = A.start, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA## Warning in min(AIC1_322$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in get(paste("nls_322.", Mod.Sel1, sep = "")) :
## object 'nls_322.' not foundsummary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
- log-normal phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"- Cannot fit model
- not enough data (only 3 observations)
331 - Great Plains/Palouse Dry Steppe
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 327 230.98
## 2 326 221.26 1 9.7243 14.3276 0.0001828 ***
## 3 308 205.48 18 15.7769 1.3138 0.1767975
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3395.864
## 2 2 3383.670
## 3 3 3221.135##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 4.26044 5.00230 0.852 0.39504
## phi -0.09420 0.02031 -4.638 5.20e-06 ***
## alpha 0.71650 0.17048 4.203 3.46e-05 ***
## A 38.23376 22.39968 1.707 0.08885 .
## k 18.37690 5.72664 3.209 0.00147 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8168 on 308 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 3.76e-06
## (18 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_331, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 308 205.48
## 2 307 196.58 1 8.9062 13.909 0.0002285 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 3221.135
## 2 3a 3209.266
## 3 3b NA
## 4 3c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.72254 1.74633 0.414 0.67935
## phi -0.08876 0.02070 -4.288 2.42e-05 ***
## alpha 0.85825 0.11815 7.264 3.11e-12 ***
## A 100.86242 65.16488 1.548 0.12270
## k 119.62952 132.17299 0.905 0.36612
## p 0.19994 0.07696 2.598 0.00983 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8002 on 307 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 9.255e-06
## (18 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Error in nls(f_6, data = G_331, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: iteration limit reached without convergence (10)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 325 228.37
## 2 324 228.37 1 2.1774e-06 0 0.9986
## model AIC
## 1 3a 3209.266
## 2 4 3396.105
## 3 5 3398.105
## 4 6 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.72254 1.74633 0.414 0.67935
## phi -0.08876 0.02070 -4.288 2.42e-05 ***
## alpha 0.85825 0.11815 7.264 3.11e-12 ***
## A 100.86242 65.16488 1.548 0.12270
## k 119.62952 132.17299 0.905 0.36612
## p 0.19994 0.07696 2.598 0.00983 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8002 on 307 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 9.255e-06
## (18 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.90048, p-value = 1.769e-13
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -5.7492, p-value = 8.966e-09
## alternative hypothesis: two.sidedpredict and plot
plotting 2
* Cannot fit model
332 - Great Plains Steppe
model selection 1
## Error in nls(f_1, data = G_332, start = c(ge = ge.start, A = A.start, :
## singular gradient
## Error in nls(f_2, data = G_332, start = c(ge = ge.start, phi = phi.start, :
## singular gradient
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 2128.795##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.02847 2.21721 0.464 0.64328
## phi -0.01127 0.03204 -0.352 0.72537
## alpha 0.80688 0.30138 2.677 0.00807 **
## A 385.25740 387.86420 0.993 0.32183
## k 276.62580 301.37090 0.918 0.35983
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8067 on 191 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.576e-06
## (36 observations deleted due to missingness)summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_332, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_332, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 3 2128.795
## 2 3a NA
## 3 3b NA
## 4 3c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.02847 2.21721 0.464 0.64328
## phi -0.01127 0.03204 -0.352 0.72537
## alpha 0.80688 0.30138 2.677 0.00807 **
## A 385.25740 387.86420 0.993 0.32183
## k 276.62580 301.37090 0.918 0.35983
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8067 on 191 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.576e-06
## (36 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 225 139.58
## 2 224 139.58 1 0.000 0.0000 1.0000
## 3 189 115.51 35 24.075 1.1255 0.3019
## model AIC
## 1 3 2128.795
## 2 4 2445.978
## 3 5 2447.978
## 4 6 2118.424##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.18136 2.27869 0.518 0.60476
## phi 0.00000 0.03192 0.000 1.00000
## alpha 0.81823 0.23985 3.411 0.00079 ***
## a 25.78527 12.60017 2.046 0.04210 *
## b 77.36146 65.72373 1.177 0.24065
## c 143.44351 153.97937 0.932 0.35274
## d 1.08261 0.74704 1.449 0.14894
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7818 on 189 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (36 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.88018, p-value = 2.243e-11
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -5.5496, p-value = 2.864e-08
## alternative hypothesis: two.sidedpredict and plot
plotting 2
341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
- log-normal phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"- model not fitted because only 62 observations
predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"342 - Intermountain Semi-Desert
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
- log-normal phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"411 - Everglades
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
- log-normal phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6772 1333.1
## 2 6771 1327.8 1 5.352 27.294 1.799e-07 ***
## 3 6747 1121.9 24 205.845 51.580 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 71776.53
## 2 2 71751.27
## 3 3 70444.76##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 7.378e-01 1.631e-01 4.523 6.21e-06 ***
## phi 1.749e-02 3.545e-03 4.933 8.29e-07 ***
## alpha 8.125e-01 2.205e-02 36.852 < 2e-16 ***
## A 3.887e+02 2.185e+01 17.789 < 2e-16 ***
## k 1.763e+02 1.000e+01 17.626 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4078 on 6747 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 6.706e-06
## (26 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6747 1121.9
## 2 6746 1117.8 1 4.1104 24.807 6.495e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 70444.76
## 2 3a 70421.98
## 3 3b 70407.65
## 4 3c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s +
## STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 6.537e-01 1.575e-01 4.150 3.37e-05 ***
## phi 1.621e-02 3.525e-03 4.599 4.33e-06 ***
## alpha 8.187e-01 2.218e-02 36.910 < 2e-16 ***
## A 2.377e+02 1.599e+01 14.864 < 2e-16 ***
## k 7.376e+01 7.108e+00 10.377 < 2e-16 ***
## s 1.275e+00 4.822e-02 26.448 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4066 on 6746 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 3.339e-06
## (26 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6770 1322.9
## 2 6769 1318.2 1 4.706 24.168 9.038e-07 ***
## 3 6745 1113.3 24 204.935 51.735 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3b 70407.65
## 2 4 71728.53
## 3 5 71706.38
## 4 6 70396.58##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 6.752e-01 1.589e-01 4.249 2.18e-05 ***
## phi 1.618e-02 3.519e-03 4.598 4.34e-06 ***
## alpha 8.210e-01 2.190e-02 37.487 < 2e-16 ***
## a 1.653e+01 2.717e+00 6.084 1.24e-09 ***
## b 1.482e+02 1.019e+01 14.549 < 2e-16 ***
## c 1.995e+02 2.424e+01 8.228 2.27e-16 ***
## d 1.645e+00 1.086e-01 15.152 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4063 on 6745 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (26 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: fits
plot residuals
predict and plot
plotting 2
M221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8180 1388.9
## 2 8179 1375.5 1 13.387 79.603 < 2.2e-16 ***
## 3 8123 1262.9 56 112.597 12.933 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 90550.28
## 2 2 90473.02
## 3 3 89329.70##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.175313 0.144300 8.145 4.36e-16 ***
## phi -0.031966 0.003502 -9.127 < 2e-16 ***
## alpha 0.842348 0.033283 25.309 < 2e-16 ***
## A 239.152856 7.892077 30.303 < 2e-16 ***
## k 57.456845 2.250413 25.532 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3943 on 8123 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 2.2e-06
## (58 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8123 1262.9
## 2 8122 1262.9 1 0.006 0.0363 0.8489
## 3 8122 1256.5 0 0.000
## 4 8121 1224.6 1 31.907 211.5962 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 89329.70
## 2 3a 89331.66
## 3 3b 89290.55
## 4 3c 89083.49##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.357729 0.151543 8.959 <2e-16 ***
## phi -0.031471 0.003435 -9.163 <2e-16 ***
## alpha 0.845265 0.029911 28.259 <2e-16 ***
## A 148.489315 4.499786 32.999 <2e-16 ***
## k 38.361942 0.798390 48.049 <2e-16 ***
## p 0.254305 0.013146 19.345 <2e-16 ***
## s 2.978640 0.176324 16.893 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3883 on 8121 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 3.624e-06
## (58 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8178 1358.7
## 2 8177 1358.7 1 0.00 0.000 1
## 3 8121 1234.5 56 124.24 14.595 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3c 89083.49
## 2 4 90374.77
## 3 5 90376.77
## 4 6 89148.89##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.357729 0.151543 8.959 <2e-16 ***
## phi -0.031471 0.003435 -9.163 <2e-16 ***
## alpha 0.845265 0.029911 28.259 <2e-16 ***
## A 148.489315 4.499786 32.999 <2e-16 ***
## k 38.361942 0.798390 48.049 <2e-16 ***
## p 0.254305 0.013146 19.345 <2e-16 ***
## s 2.978640 0.176324 16.893 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3883 on 8121 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 3.624e-06
## (58 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: fits
plot residuals
predict and plot
plotting 2
M223 - Ozark Broadleaf Forest Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 887 122.26
## 2 886 119.04 1 3.2238 23.995 1.148e-06 ***
## 3 881 103.70 5 15.3390 26.064 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 9055.244
## 2 2 9033.461
## 3 3 8884.472##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.48170 0.22025 -2.187 0.029 *
## phi 0.05665 0.01331 4.255 2.32e-05 ***
## alpha 0.88034 0.07223 12.188 < 2e-16 ***
## A 307.38272 34.06829 9.023 < 2e-16 ***
## k 92.08986 14.22329 6.475 1.58e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3431 on 881 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 6.302e-07
## (7 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M223, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 881 103.7
## 2 880 103.5 1 0.19217 1.6338 0.2015
## model AIC
## 1 3 8884.472
## 2 3a 8884.828
## 3 3b 8886.130
## 4 3c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.48170 0.22025 -2.187 0.029 *
## phi 0.05665 0.01331 4.255 2.32e-05 ***
## alpha 0.88034 0.07223 12.188 < 2e-16 ***
## A 307.38272 34.06829 9.023 < 2e-16 ***
## k 92.08986 14.22329 6.475 1.58e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3431 on 881 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 6.302e-07
## (7 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 885 121.92
## 2 884 118.67 1 3.2543 24.242 1.014e-06 ***
## 3 879 103.55 5 15.1183 25.667 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 8884.472
## 2 4 9056.791
## 3 5 9034.713
## 4 6 8887.220##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.48170 0.22025 -2.187 0.029 *
## phi 0.05665 0.01331 4.255 2.32e-05 ***
## alpha 0.88034 0.07223 12.188 < 2e-16 ***
## A 307.38272 34.06829 9.023 < 2e-16 ***
## k 92.08986 14.22329 6.475 1.58e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3431 on 881 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 6.302e-07
## (7 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96281, p-value = 3.117e-14
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -13.76, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M231 - Ouachita Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1005 242.87
## 2 1004 242.30 1 0.5714 2.3678 0.1242
## 3 990 213.67 14 28.6282 9.4747 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 10414.94
## 2 2 10414.56
## 3 3 10207.82##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 6.345e-01 5.315e-01 1.194 0.233
## phi 3.774e-03 1.472e-02 0.256 0.798
## alpha 7.252e-01 6.819e-02 10.636 < 2e-16 ***
## A 2.251e+02 3.098e+01 7.267 7.46e-13 ***
## k 8.717e+01 1.169e+01 7.459 1.91e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4646 on 990 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.806e-06
## (14 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 990 213.67
## 2 989 212.14 1 1.52740 7.1208 0.007744 **
## 3 989 212.14 0 0.00000
## 4 988 212.12 1 0.02084 0.0971 0.755417
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 10207.82
## 2 3a 10202.68
## 3 3b 10202.66
## 4 3c 10204.57##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s +
## STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 5.442e-01 5.113e-01 1.064 0.287
## phi 3.429e-03 1.470e-02 0.233 0.816
## alpha 7.388e-01 6.391e-02 11.561 < 2e-16 ***
## A 6.025e+03 8.360e+04 0.072 0.943
## k 2.222e+04 4.647e+05 0.048 0.962
## s 7.043e-01 1.107e-01 6.363 3.02e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4631 on 989 degrees of freedom
##
## Number of iterations to convergence: 16
## Achieved convergence tolerance: 4.751e-06
## (14 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Error in nls(f_6, data = G_M231, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: iteration limit reached without convergence (10)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1003 242.05
## 2 1002 241.48 1 0.57363 2.3802 0.1232
## model AIC
## 1 3b 10202.66
## 2 4 10415.55
## 3 5 10415.16
## 4 6 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s +
## STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 5.442e-01 5.113e-01 1.064 0.287
## phi 3.429e-03 1.470e-02 0.233 0.816
## alpha 7.388e-01 6.391e-02 11.561 < 2e-16 ***
## A 6.025e+03 8.360e+04 0.072 0.943
## k 2.222e+04 4.647e+05 0.048 0.962
## s 7.043e-01 1.107e-01 6.363 3.02e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4631 on 989 degrees of freedom
##
## Number of iterations to convergence: 16
## Achieved convergence tolerance: 4.751e-06
## (14 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96071, p-value = 1.042e-15
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -13.329, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M242 - Cascade Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3298 2133.7
## 2 3297 2133.5 1 0.185 0.2856 0.5931
## 3 3223 1973.9 74 159.675 3.5233 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 43707.67
## 2 2 43709.38
## 3 3 42726.34##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -3.865e-01 4.503e-01 -0.858 0.391
## phi 7.455e-03 1.536e-02 0.485 0.627
## alpha 1.048e+00 6.743e-02 15.534 < 2e-16 ***
## A 1.204e+03 1.796e+02 6.702 2.41e-11 ***
## k 3.384e+02 3.148e+01 10.750 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7826 on 3223 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 2.764e-06
## (75 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3223 1973.9
## 2 3222 1944.4 1 29.448 48.796 3.435e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 42726.34
## 2 3a 42679.82
## 3 3b NA
## 4 3c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.286311 0.468612 -0.611 0.541
## phi 0.001043 0.015220 0.069 0.945
## alpha 1.094399 0.065937 16.598 < 2e-16 ***
## A 886.863086 131.191842 6.760 1.63e-11 ***
## k 183.453925 21.899737 8.377 < 2e-16 ***
## p -0.050509 0.011006 -4.589 4.62e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7768 on 3222 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 5.33e-06
## (75 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3296 2088.0
## 2 3295 2088.0 1 0.00 0.0000 1
## 3 3221 1937.6 74 150.37 3.3781 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3a 42679.82
## 2 4 43640.14
## 3 5 43642.14
## 4 6 42670.50##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.27245 0.47058 -0.579 0.563
## phi 0.00000 0.01519 0.000 1.000
## alpha 1.08485 0.06785 15.990 < 2e-16 ***
## a 8.65674 10.66920 0.811 0.417
## b 568.18302 85.65471 6.633 3.83e-11 ***
## c 556.00850 107.68623 5.163 2.57e-07 ***
## d 2.03645 0.16934 12.026 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7756 on 3221 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (75 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94604, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -16.722, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1983 1184.82
## 2 1982 1086.49 1 98.334 179.3835 <2e-16 ***
## 3 1698 969.05 284 117.440 0.7246 0.9997
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 24895.19
## 2 2 24725.12
## 3 3 21327.35##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.15844 0.33074 -3.503 0.000473 ***
## phi 0.20254 0.01308 15.487 < 2e-16 ***
## alpha 0.75554 0.10170 7.429 1.72e-13 ***
## A 858.62930 116.97742 7.340 3.29e-13 ***
## k 131.30793 16.80895 7.812 9.80e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7554 on 1698 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 4.086e-07
## (290 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1698 969.05
## 2 1697 968.64 1 0.40720 0.7134 0.3984
## 3 1697 968.83 0 0.00000
## 4 1696 968.60 1 0.23227 0.4067 0.5237
## model AIC
## 1 3 21327.35
## 2 3a 21328.64
## 3 3b 21328.98
## 4 3c 21330.57##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.15844 0.33074 -3.503 0.000473 ***
## phi 0.20254 0.01308 15.487 < 2e-16 ***
## alpha 0.75554 0.10170 7.429 1.72e-13 ***
## A 858.62930 116.97742 7.340 3.29e-13 ***
## k 131.30793 16.80895 7.812 9.80e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7554 on 1698 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 4.086e-07
## (290 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1981 1183.63
## 2 1980 1084.37 1 99.26 181.2432 <2e-16 ***
## 3 1696 968.78 284 115.59 0.7125 0.9998
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 21327.35
## 2 4 24897.19
## 3 5 24725.25
## 4 6 21330.89##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.15844 0.33074 -3.503 0.000473 ***
## phi 0.20254 0.01308 15.487 < 2e-16 ***
## alpha 0.75554 0.10170 7.429 1.72e-13 ***
## A 858.62930 116.97742 7.340 3.29e-13 ***
## k 131.30793 16.80895 7.812 9.80e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7554 on 1698 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 4.086e-07
## (290 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.89658, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.3916, p-value = 1.125e-05
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M262 - California coastal range - coniferous forest - open woodland - shrub meadow
Model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
- log-normal phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"- model can fit - but K is negative (only 19 observations) - model excluded
predict and plot
## [1] "cannot plot data with prediction"plotting 2
M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 363 122.71
## 2 362 120.40 1 2.3108 6.9479 0.008753 **
## 3 360 116.95 2 3.4501 5.3102 0.005336 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3833.912
## 2 2 3828.954
## 3 3 3813.507##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.79971 0.34921 -5.154 4.22e-07 ***
## phi 0.05202 0.02186 2.379 0.01786 *
## alpha 0.51051 0.14684 3.477 0.00057 ***
## A 571.89280 200.04822 2.859 0.00450 **
## k 207.88399 95.57943 2.175 0.03028 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.57 on 360 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 4.209e-06
## (2 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_M313, :
## number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 360 116.95
## 2 359 115.13 1 1.8152 5.6599 0.01788 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 3813.507
## 2 3a 3809.797
## 3 3b NA
## 4 3c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.81719 0.33976 -5.349 1.58e-07 ***
## phi 0.05053 0.02187 2.310 0.0215 *
## alpha 0.55632 0.13755 4.045 6.42e-05 ***
## A 1053.49011 935.16228 1.127 0.2607
## k 553.32368 612.06966 0.904 0.3666
## p 0.02699 0.01970 1.370 0.1717
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5663 on 359 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 8.769e-06
## (2 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 361 120.72
## 2 360 118.33 1 2.3867 7.2613 0.0073760 **
## 3 358 113.12 2 5.2114 8.2467 0.0003152 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3a 3809.797
## 2 4 3831.912
## 3 5 3826.603
## 4 6 3805.346##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.64684 0.39761 -4.142 4.30e-05 ***
## phi 0.04942 0.02191 2.255 0.024706 *
## alpha 0.58276 0.13139 4.435 1.23e-05 ***
## a 49.30946 12.91826 3.817 0.000159 ***
## b 182.53573 43.85848 4.162 3.96e-05 ***
## c 174.61256 38.10635 4.582 6.36e-06 ***
## d 0.95327 0.19974 4.773 2.65e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5621 on 358 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.9444, p-value = 1.805e-10
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = 0.0034951, p-value = 0.9972
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1736 651.22
## 2 1735 650.35 1 0.875 2.3355 0.1266
## 3 1713 585.52 22 64.825 8.6205 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 18138.23
## 2 2 18137.89
## 3 3 17801.62##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.86844 0.34495 -2.518 0.0119 *
## phi 0.02219 0.01101 2.014 0.0441 *
## alpha 0.61462 0.04179 14.707 < 2e-16 ***
## A 264.86669 35.08407 7.549 7.06e-14 ***
## k 114.94824 11.56820 9.937 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5846 on 1713 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 2.39e-06
## (39 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Warning in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M331, : No starting values specified for some parameters.
## Initializing 'ge', 'phi', 'p', 'A', 's', 'k' to '1.'.
## Consider specifying 'start' or using a selfStart model## Error in model.frame.default(formula = ~B_plt_t2_MgHa + MEASTIME_t2 + :
## variable lengths differ (found for '(sstart)')
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1713 585.52
## 2 1712 579.19 1 6.3281 18.705 1.614e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 17801.62
## 2 3a 17784.95
## 3 3b 17795.30
## 4 3c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.841945 0.348432 -2.416 0.0158 *
## phi 0.022076 0.010982 2.010 0.0446 *
## alpha 0.629831 0.039965 15.760 < 2e-16 ***
## A 338.896959 58.574560 5.786 8.57e-09 ***
## k 209.274046 46.773721 4.474 8.18e-06 ***
## p 0.043809 0.007593 5.770 9.40e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5816 on 1712 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 5.915e-06
## (39 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1734 645.18
## 2 1733 644.14 1 1.038 2.7914 0.09495 .
## 3 1711 571.23 22 72.908 9.9264 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3a 17784.95
## 2 4 18126.02
## 3 5 18125.22
## 4 6 17763.18##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.88397 0.33594 -2.631 0.00858 **
## phi 0.02721 0.01079 2.523 0.01174 *
## alpha 0.64195 0.03893 16.490 < 2e-16 ***
## a 36.52027 5.02663 7.265 5.63e-13 ***
## b 130.94864 16.75863 7.814 9.61e-15 ***
## c 217.30447 25.55815 8.502 < 2e-16 ***
## d 1.30810 0.11645 11.233 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5778 on 1711 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (39 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.9253, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -5.8651, p-value = 4.49e-09
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2617 1396.7
## 2 2616 1389.5 1 7.179 13.5148 0.0002415 ***
## 3 2520 1269.0 96 120.535 2.4933 2.212e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 28732.83
## 2 2 28721.33
## 3 3 27762.82##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.92778 0.90712 1.023 0.30651
## phi 0.04066 0.01473 2.761 0.00581 **
## alpha 0.52784 0.05007 10.542 < 2e-16 ***
## A 170.06337 34.02318 4.998 6.18e-07 ***
## k 91.15763 7.90387 11.533 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7096 on 2520 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.741e-06
## (96 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2520 1269.0
## 2 2519 1233.3 1 35.669 72.851 < 2.2e-16 ***
## 3 2519 1250.6 0 0.000
## 4 2518 1207.9 1 42.677 88.963 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 27762.82
## 2 3a 27692.83
## 3 3b 27727.95
## 4 3c 27642.27##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.02638 0.92599 1.108 0.267786
## phi 0.04879 0.01397 3.491 0.000489 ***
## alpha 0.63236 0.03933 16.080 < 2e-16 ***
## A 130.40594 27.04390 4.822 1.51e-06 ***
## k 80.53724 5.47767 14.703 < 2e-16 ***
## p 0.18868 0.01733 10.885 < 2e-16 ***
## s 2.44328 0.29717 8.222 3.17e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6926 on 2518 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 6.271e-06
## (96 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2615 1381.0
## 2 2614 1373.9 1 7.022 13.3599 0.0002621 ***
## 3 2518 1205.7 96 168.228 3.6596 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3c 27642.27
## 2 4 28707.13
## 3 5 28695.77
## 4 6 27637.65##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.04310 0.92937 1.122 0.261811
## phi 0.04819 0.01397 3.449 0.000572 ***
## alpha 0.63571 0.03890 16.341 < 2e-16 ***
## a 24.94418 4.99508 4.994 6.33e-07 ***
## b 94.74616 19.17706 4.941 8.30e-07 ***
## c 212.83670 20.85680 10.205 < 2e-16 ***
## d 1.25548 0.10079 12.456 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.692 on 2518 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (96 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.90038, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.5324, p-value = 5.832e-06
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1753 893.12
## 2 1752 890.18 1 2.932 5.7696 0.01641 *
## 3 1692 797.00 60 93.185 3.2972 1.842e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 19820.05
## 2 2 19816.27
## 3 3 19156.50##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.58609 1.60789 0.986 0.32406
## phi 0.04951 0.01870 2.647 0.00819 **
## alpha 0.65188 0.05503 11.847 < 2e-16 ***
## A 267.34611 83.33113 3.208 0.00136 **
## k 164.02805 18.86160 8.696 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6863 on 1692 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 4.786e-06
## (61 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1692 797.00
## 2 1691 789.13 1 7.8716 16.868 4.199e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 19156.50
## 2 3a 19141.65
## 3 3b NA
## 4 3c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.73215 1.69289 1.023 0.30636
## phi 0.05386 0.01852 2.909 0.00368 **
## alpha 0.66456 0.05087 13.063 < 2e-16 ***
## A 329.90306 113.14657 2.916 0.00360 **
## k 257.91420 61.78254 4.175 3.14e-05 ***
## p 0.01881 0.00391 4.810 1.64e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6831 on 1691 degrees of freedom
##
## Number of iterations to convergence: 45
## Achieved convergence tolerance: 9.406e-06
## (61 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1751 828.43
## 2 1750 827.20 1 1.231 2.604 0.1068
## 3 1690 713.90 60 113.295 4.470 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3a 19141.65
## 2 4 19692.03
## 3 5 19691.41
## 4 6 18973.65##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.25857 1.89702 1.191 0.23398
## phi 0.02796 0.01763 1.586 0.11296
## alpha 0.70224 0.04134 16.985 < 2e-16 ***
## a 19.07334 6.06344 3.146 0.00169 **
## b 92.37563 29.34522 3.148 0.00167 **
## c 132.62275 5.79400 22.890 < 2e-16 ***
## d 0.96331 0.04975 19.364 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6499 on 1690 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (61 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93135, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.6964, p-value = 2.647e-06
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M334 - Black Hills Coniferous Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 443 175.53
## 2 442 175.51 1 0.022 0.0548 0.81496
## 3 345 127.57 97 47.943 1.3367 0.03139 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 4440.199
## 2 2 4442.143
## 3 3 3469.759##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.407138 1.013752 -0.402 0.688216
## phi -0.004488 0.025349 -0.177 0.859583
## alpha 0.782447 0.098140 7.973 2.3e-14 ***
## A 123.321200 35.167088 3.507 0.000514 ***
## k 63.554870 21.063832 3.017 0.002740 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6081 on 345 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.602e-06
## (101 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 345 127.57
## 2 344 127.57 1 0.0009742 0.0026 0.9592
## 3 344 127.56 0 0.0000000
## 4 343 127.53 1 0.0262299 0.0705 0.7907
## model AIC
## 1 3 3469.759
## 2 3a 3471.757
## 3 3b 3471.734
## 4 3c 3473.662##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.407138 1.013752 -0.402 0.688216
## phi -0.004488 0.025349 -0.177 0.859583
## alpha 0.782447 0.098140 7.973 2.3e-14 ***
## A 123.321200 35.167088 3.507 0.000514 ***
## k 63.554870 21.063832 3.017 0.002740 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6081 on 345 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.602e-06
## (101 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 441 174.96
## 2 440 174.96 1 0.000 0.0000 1.00000
## 3 343 127.61 97 47.344 1.3119 0.04106 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 3469.759
## 2 4 4442.739
## 3 5 4444.739
## 4 6 3473.887##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.407138 1.013752 -0.402 0.688216
## phi -0.004488 0.025349 -0.177 0.859583
## alpha 0.782447 0.098140 7.973 2.3e-14 ***
## A 123.321200 35.167088 3.507 0.000514 ***
## k 63.554870 21.063832 3.017 0.002740 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6081 on 345 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.602e-06
## (101 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93506, p-value = 3.149e-11
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -5.9043, p-value = 3.541e-09
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 214 80.493
## 2 213 80.461 1 0.0328 0.0868 0.768564
## 3 209 74.179 4 6.2812 4.4243 0.001875 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 2156.928
## 2 2 2158.840
## 3 3 2125.348##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.51386 0.56712 -2.669 0.008196 **
## phi -0.03783 0.06907 -0.548 0.584493
## alpha 0.52145 0.13802 3.778 0.000206 ***
## A 202.94010 57.18345 3.549 0.000478 ***
## k 88.38698 23.66402 3.735 0.000242 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5958 on 209 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 9.271e-06
## (6 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 209 74.179
## 2 208 73.531 1 0.6482 1.8337 0.177163
## 3 208 74.085 0 0.0000
## 4 207 70.803 1 3.2811 9.5927 0.002224 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 2125.348
## 2 3a 2125.470
## 3 3b 2127.075
## 4 3c 2119.380##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.53631 0.53781 -2.857 0.004719 **
## phi -0.03188 0.06598 -0.483 0.629538
## alpha 0.56263 0.12916 4.356 2.08e-05 ***
## A 142.47922 37.97167 3.752 0.000228 ***
## k 66.69676 9.16110 7.280 6.81e-12 ***
## p 0.18019 0.03962 4.548 9.22e-06 ***
## s 3.04230 1.23140 2.471 0.014297 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5848 on 207 degrees of freedom
##
## Number of iterations to convergence: 15
## Achieved convergence tolerance: 5.393e-06
## (6 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 212 76.519
## 2 211 76.519 1 0.0000 0.0000 1.000000
## 3 207 70.029 4 6.4896 4.7956 0.001015 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3c 2119.380
## 2 4 2149.940
## 3 5 2151.940
## 4 6 2117.028##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.62316 0.50044 -3.243 0.001377 **
## phi 0.00000 0.06252 0.000 1.000000
## alpha 0.54428 0.13036 4.175 4.38e-05 ***
## a 27.41737 7.63476 3.591 0.000411 ***
## b 116.77576 28.20651 4.140 5.05e-05 ***
## c 155.67685 22.11390 7.040 2.78e-11 ***
## d 1.03563 0.19858 5.215 4.44e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5816 on 207 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (6 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
- log-normal phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93333, p-value = 2.665e-08
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -1.0322, p-value = 0.302
## alternative hypothesis: two.sidedpredict and plot
plotting 2
Fitted parameters
Best / selected models by ecoprovince
| Code | Ecoregion | Sel.Mod.2 | Sel.Mod.3 | Best.Mod |
|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | 3 | 6 | 6 |
| 212 | Laurentian Mixed Forest | 3a | 6 | 6 |
| 221 | Eastern Broadleaf Forest | 3b | 6 | 6 |
| 222 | Midwest Broadleaf Forest | 3b | 6 | 6 |
| 223 | Central Interior Broadleaf Forest | 3b | 6 | 6 |
| 231 | Southeastern Mixed Forest | 3c | 6 | 6 |
| 232 | Outer Coastal Plain Mixed Forest | 3a | 6 | 6 |
| 234 | Lower Mississippi Riverine Forest | 3 | 3 | 3 |
| 242 | Pacific Lowland Mixed Forest | NA | NA | NA |
| 251 | Prairie Parkland (Temperate) | 3b | 6 | 6 |
| 255 | Prairie Parkland (Subtropical) | 3a | 6 | 6 |
| 261 | California Coastal Chaparral Forest and Shrub | NA | NA | NA |
| 262 | California Dry Steppe | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | 3a | 3a | 3a |
| 313 | Colorado Plateau Semi-Desert | 3 | 6 | 6 |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | NA | NA | NA |
| 322 | American Semidesert and Desert | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | 3a | 3a | 3a |
| 332 | Great Plains Steppe | 3 | 6 | 6 |
| 341 | Intermountain Semi-Desert and Desert | NA | NA | NA |
| 342 | Intermountain Semi-Desert | NA | NA | NA |
| 411 | Everglades | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | 3b | 6 | 6 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | 3c | 3c | 3c |
| M223 | Ozark Broadleaf Forest Meadow | 3 | 3 | 3 |
| M231 | Ouachita Mixed Forest | 3b | 3b | 3b |
| M242 | Cascade Mixed Forest | 3a | 6 | 6 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | 3 | 3 | 3 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | 3a | 6 | 6 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | 3a | 6 | 6 |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 3c | 6 | 6 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 3a | 6 | 6 |
| M334 | Black Hills Coniferous Forest | 3 | 3 | 3 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | 3c | 6 | 6 |
table by ecoprovince
| Code | Ecoregion | region | n.obs | n.plots | ge | ge.variance | ge.2.5 | ge.97.5 | phi | phi.variance | phi.2.5 | phi.97.5 | alpha | alpha.variance | alpha.2.5 | alpha.97.5 | A | A.2.5 | A.97.5 | k | k.2.5 | k.97.5 | a | a.2.5 | a.97.5 | b | b.se | b.2.5 | b.97.5 | c | c.2.5 | c.97.5 | d | d.2.5 | d.97.5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | east | 6884 | 2879 | 0.8813298 | 0.0385461 | 0.4964587 | 1.2662009 | 0.0000000 | 0.0000166 | -0.0079834 | 0.0079834 | 0.8426527 | 0.0007101 | 0.7904150 | 0.8948904 | 387.2824 | 339.80547 | 434.7593 | 170.93933 | 1.482754e+02 | 193.60327 | 37.964963 | 34.6005556 | 41.32937 | 102.86037 | NA | 93.69637 | 112.02437 | 114.69626 | 106.42497 | 122.96755 | 0.9253480 | 0.8481489 | 1.0025471 |
| 212 | Laurentian Mixed Forest | east | 22685 | 9493 | 0.4140232 | 0.0135036 | 0.1862505 | 0.6417958 | 0.0079614 | 0.0000077 | 0.0025056 | 0.0134171 | 0.7834429 | 0.0002186 | 0.7544657 | 0.8124202 | 230.0844 | 208.94713 | 251.2217 | 122.01600 | 1.050630e+02 | 138.96896 | 23.935105 | 22.5724057 | 25.29780 | 80.31661 | NA | 76.05026 | 84.58296 | 109.65272 | 103.79840 | 115.50703 | 1.1955780 | 1.1383684 | 1.2527877 |
| 221 | Eastern Broadleaf Forest | east | 7307 | 3560 | 0.1820948 | 0.0151020 | -0.0588062 | 0.4229959 | 0.0000000 | 0.0000113 | -0.0065768 | 0.0065768 | 0.8234610 | 0.0006287 | 0.7743096 | 0.8726124 | 328.1596 | 279.12094 | 377.1982 | 75.60570 | 5.893544e+01 | 92.27596 | 30.305358 | 26.2700899 | 34.34063 | 165.27209 | NA | 150.56033 | 179.98385 | 136.54946 | 118.54115 | 154.55777 | 1.3442416 | 1.2204524 | 1.4680308 |
| 222 | Midwest Broadleaf Forest | east | 5846 | 2589 | -0.1604805 | 0.0364924 | -0.5349856 | 0.2140247 | 0.0293096 | 0.0000649 | 0.0135116 | 0.0451077 | 0.8611978 | 0.0012151 | 0.7928601 | 0.9295355 | 254.4786 | 204.21299 | 304.7443 | 74.31014 | 5.401579e+01 | 94.60449 | 26.981911 | 23.8644488 | 30.09937 | 117.43133 | NA | 106.63587 | 128.22678 | 102.33991 | 93.72365 | 110.95617 | 1.0169469 | 0.9281184 | 1.1057755 |
| 223 | Central Interior Broadleaf Forest | east | 10006 | 3860 | 0.1196577 | 0.0124990 | -0.0994946 | 0.3388099 | 0.0000000 | 0.0000176 | -0.0082323 | 0.0082323 | 0.7696807 | 0.0006790 | 0.7186006 | 0.8207608 | 173.7654 | 157.98769 | 189.5431 | 40.14399 | 3.515267e+01 | 45.13530 | 31.403491 | 27.5825784 | 35.22440 | 103.16963 | NA | 96.31482 | 110.02444 | 102.24776 | 94.39256 | 110.10295 | 1.2127052 | 1.1106756 | 1.3147348 |
| 231 | Southeastern Mixed Forest | east | 12844 | 5935 | 2.1217165 | 0.0355755 | 1.7520030 | 2.4914300 | 0.0000000 | 0.0000134 | -0.0071633 | 0.0071633 | 0.8065997 | 0.0001042 | 0.7865876 | 0.8266117 | 126.5825 | 117.51179 | 135.6532 | 32.08316 | 3.036956e+01 | 33.79675 | 26.098675 | 24.5400334 | 27.65732 | 97.84423 | NA | 90.20193 | 105.48654 | 101.68725 | 90.77491 | 112.59959 | 1.3833389 | 1.2911898 | 1.4754880 |
| 232 | Outer Coastal Plain Mixed Forest | east | 13167 | 6463 | 1.3225831 | 0.0321247 | 0.9712581 | 1.6739081 | 0.0223844 | 0.0000178 | 0.0141249 | 0.0306439 | 0.8716493 | 0.0000685 | 0.8554209 | 0.8878777 | 685.0304 | 431.48304 | 938.5778 | 384.89604 | 2.116345e+02 | 558.15754 | 32.786968 | 30.6808067 | 34.89313 | 104.58378 | NA | 95.18145 | 113.98612 | 106.22272 | 92.62807 | 119.81737 | 1.3231333 | 1.2164743 | 1.4297923 |
| 234 | Lower Mississippi Riverine Forest | east | 1344 | 759 | 0.0553654 | 0.1712485 | -0.7564800 | 0.8672107 | 0.0217006 | 0.0002104 | -0.0067569 | 0.0501580 | 0.6620878 | 0.0029326 | 0.5558480 | 0.7683275 | 550.8414 | 366.92569 | 734.7570 | 164.62568 | 1.030939e+02 | 226.15747 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 242 | Pacific Lowland Mixed Forest | pacific | 85 | 85 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 251 | Prairie Parkland (Temperate) | east | 2290 | 903 | 0.3166112 | 0.0992728 | -0.3013470 | 0.9345694 | 0.0000000 | 0.0000700 | -0.0164080 | 0.0164080 | 0.7210026 | 0.0043343 | 0.5918790 | 0.8501261 | 145.0376 | 118.32125 | 171.7540 | 38.92230 | 3.202015e+01 | 45.82444 | 26.749847 | 19.1336653 | 34.36603 | 93.30996 | NA | 78.42397 | 108.19596 | 99.58963 | 86.01890 | 113.16036 | 1.0975156 | 0.9137136 | 1.2813176 |
| 255 | Prairie Parkland (Subtropical) | east | 714 | 318 | -0.1859521 | 0.1765241 | -1.0109372 | 0.6390330 | 0.0000000 | 0.0002155 | -0.0288221 | 0.0288221 | 0.6430370 | 0.0060449 | 0.4903726 | 0.7957013 | 266.5110 | 97.32554 | 435.6964 | 119.97203 | 5.086584e+00 | 234.85747 | 22.558489 | 16.9617842 | 28.15519 | 75.97870 | NA | 59.18193 | 92.77547 | 59.50946 | 48.79835 | 70.22057 | 0.9985524 | 0.7736257 | 1.2234791 |
| 261 | California Coastal Chaparral Forest and Shrub | pacific | 26 | 26 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 262 | California Dry Steppe | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | pacific | 159 | 157 | -0.0777708 | 1.6428227 | -2.6104792 | 2.4549376 | -0.0271234 | 0.0044972 | -0.1596371 | 0.1053903 | 0.8592773 | 0.0576453 | 0.3848478 | 1.3337067 | 19316.5492 | -21300.54714 | 59933.6456 | 4915.53636 | -6.143886e+03 | 15974.95866 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 313 | Colorado Plateau Semi-Desert | interior west | 218 | 218 | -1.2871343 | 0.4558669 | -2.6182059 | 0.0439372 | 0.0322690 | 0.0012367 | -0.0370586 | 0.1015966 | 0.2997387 | 0.0606681 | -0.1858431 | 0.7853205 | 258.0581 | 55.41657 | 460.6996 | 135.22109 | 2.508344e+01 | 245.35873 | 53.322071 | 21.1701179 | 85.47402 | 144.62680 | NA | 61.50967 | 227.74393 | 139.92344 | 125.13669 | 154.71018 | 0.5729363 | 0.4034699 | 0.7424026 |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | interior west | 4 | 4 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | interior west | 9 | 9 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 322 | American Semidesert and Desert | interior west | 3 | 3 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | interior west | 331 | 255 | 0.7225403 | 3.0496758 | -2.7137545 | 4.1588352 | -0.0887580 | 0.0004285 | -0.1294900 | -0.0480260 | 0.8582539 | 0.0139587 | 0.6257737 | 1.0907341 | 100.8624 | -27.36391 | 229.0887 | 119.62952 | -1.404501e+02 | 379.70913 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 332 | Great Plains Steppe | interior west | 232 | 128 | 1.1813563 | 5.1924335 | -3.3135787 | 5.6762913 | 0.0000000 | 0.0010189 | -0.0629659 | 0.0629659 | 0.8182331 | 0.0575269 | 0.3451107 | 1.2913554 | 385.2574 | -379.78999 | 1150.3048 | 276.62580 | -3.178168e+02 | 871.06845 | 25.785272 | 0.9302398 | 50.64030 | 77.36146 | NA | -52.28485 | 207.00776 | 143.44351 | -160.29543 | 447.18245 | 1.0826067 | -0.3909927 | 2.5562062 |
| 341 | Intermountain Semi-Desert and Desert | interior west | 66 | 64 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 342 | Intermountain Semi-Desert | interior west | 124 | 123 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 411 | Everglades | east | 96 | 63 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | east | 6778 | 3008 | 0.6752105 | 0.0252576 | 0.3636647 | 0.9867562 | 0.0161825 | 0.0000124 | 0.0092833 | 0.0230816 | 0.8210021 | 0.0004796 | 0.7780697 | 0.8639346 | 237.6527 | 206.30929 | 268.9961 | 73.75687 | 5.982324e+01 | 87.69050 | 16.530726 | 11.2043078 | 21.85714 | 148.22719 | NA | 128.25566 | 168.19872 | 199.46105 | 151.93778 | 246.98431 | 1.6450846 | 1.4322431 | 1.8579262 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | east | 8186 | 3765 | 1.3577291 | 0.0229653 | 1.0606656 | 1.6547926 | -0.0314710 | 0.0000118 | -0.0382038 | -0.0247381 | 0.8452651 | 0.0008947 | 0.7866320 | 0.9038982 | 148.4893 | 139.66858 | 157.3100 | 38.36194 | 3.679689e+01 | 39.92699 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M223 | Ozark Broadleaf Forest Meadow | east | 893 | 348 | -0.4816973 | 0.0485101 | -0.9139735 | -0.0494211 | 0.0566491 | 0.0001773 | 0.0305163 | 0.0827820 | 0.8803414 | 0.0052175 | 0.7385740 | 1.0221089 | 307.3827 | 240.51824 | 374.2472 | 92.08986 | 6.417436e+01 | 120.00535 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M231 | Ouachita Mixed Forest | east | 1009 | 496 | 0.5442074 | 0.2614686 | -0.4592286 | 1.5476434 | 0.0034292 | 0.0002162 | -0.0254238 | 0.0322823 | 0.7387797 | 0.0040838 | 0.6133752 | 0.8641841 | 6025.0050 | -158038.39151 | 170088.4016 | 22220.86563 | -8.897138e+05 | 934155.54195 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M242 | Cascade Mixed Forest | pacific | 3303 | 3286 | -0.2724529 | 0.2214455 | -1.1951194 | 0.6502136 | 0.0000000 | 0.0002309 | -0.0297909 | 0.0297909 | 1.0848472 | 0.0046031 | 0.9518213 | 1.2178730 | 886.8631 | 629.63517 | 1144.0910 | 183.45392 | 1.405151e+02 | 226.39275 | 8.656743 | -12.2623717 | 29.57586 | 568.18302 | NA | 400.23976 | 736.12627 | 556.00850 | 344.86803 | 767.14898 | 2.0364456 | 1.7044233 | 2.3684679 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | pacific | 1993 | 1828 | -1.1584426 | 0.1093862 | -1.8071353 | -0.5097499 | 0.2025361 | 0.0001710 | 0.1768858 | 0.2281863 | 0.7555371 | 0.0103421 | 0.5560744 | 0.9549997 | 858.6293 | 629.19423 | 1088.0644 | 131.30793 | 9.833949e+01 | 164.27638 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | interior west | 30 | 26 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 367 | 367 | -1.6468449 | 0.1214047 | -2.4287938 | -0.8648960 | 0.0494208 | 0.0004801 | 0.0063297 | 0.0925119 | 0.5827595 | 0.0172642 | 0.3243598 | 0.8411592 | 1053.4901 | -785.59435 | 2892.5746 | 553.32368 | -6.503688e+02 | 1757.01616 | 49.309457 | 23.9042394 | 74.71467 | 182.53573 | NA | 96.28308 | 268.78837 | 174.61256 | 99.67213 | 249.55299 | 0.9532734 | 0.5604644 | 1.3460824 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 1757 | 1757 | -0.8839650 | 0.1128560 | -1.5428624 | -0.2250677 | 0.0272120 | 0.0001164 | 0.0060536 | 0.0483704 | 0.6419474 | 0.0015156 | 0.5655916 | 0.7183033 | 338.8970 | 224.01171 | 453.7822 | 209.27405 | 1.175344e+02 | 301.01371 | 36.520268 | 26.6612796 | 46.37926 | 130.94864 | NA | 98.07908 | 163.81820 | 217.30447 | 167.17596 | 267.43298 | 1.3081017 | 1.0797090 | 1.5364944 |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 2621 | 2611 | 1.0431021 | 0.8637332 | -0.7793105 | 2.8655147 | 0.0481868 | 0.0001952 | 0.0207895 | 0.0755841 | 0.6357063 | 0.0015134 | 0.5594212 | 0.7119914 | 130.4059 | 77.37537 | 183.4365 | 80.53724 | 6.979605e+01 | 91.27844 | 24.944176 | 15.1493007 | 34.73905 | 94.74616 | NA | 57.14173 | 132.35059 | 212.83670 | 171.93847 | 253.73493 | 1.2554814 | 1.0578418 | 1.4531210 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 1758 | 1747 | 2.2585657 | 3.5986739 | -1.4621843 | 5.9793156 | 0.0279551 | 0.0003107 | -0.0066193 | 0.0625294 | 0.7022357 | 0.0017093 | 0.6211452 | 0.7833262 | 329.9031 | 107.98100 | 551.8251 | 257.91420 | 1.367359e+02 | 379.09250 | 19.073342 | 7.1806968 | 30.96599 | 92.37563 | NA | 34.81883 | 149.93243 | 132.62275 | 121.25858 | 143.98692 | 0.9633133 | 0.8657379 | 1.0608888 |
| M334 | Black Hills Coniferous Forest | interior west | 451 | 179 | -0.4071378 | 1.0276930 | -2.4010500 | 1.5867743 | -0.0044877 | 0.0006426 | -0.0543455 | 0.0453701 | 0.7824467 | 0.0096315 | 0.5894184 | 0.9754750 | 123.3212 | 54.15232 | 192.4901 | 63.55487 | 2.212518e+01 | 104.98456 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | interior west | 220 | 220 | -1.6231596 | 0.2504413 | -2.6097745 | -0.6365448 | 0.0000000 | 0.0039085 | -0.1232539 | 0.1232539 | 0.5442843 | 0.0169925 | 0.2872899 | 0.8012788 | 142.4792 | 67.61844 | 217.3400 | 66.69676 | 4.863574e+01 | 84.75777 | 27.417368 | 12.3655141 | 42.46922 | 116.77576 | NA | 61.16691 | 172.38462 | 155.67685 | 112.07951 | 199.27419 | 1.0356338 | 0.6441368 | 1.4271308 |
plot ge
map
## OGR data source with driver: ESRI Shapefile
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings: PROVINCE_ PROVINCE_I
plot phi (effect of DeltaPDSI)
plot alpha (biomass compensation effect)
plot A (asymptote of B)
## Warning: Removed 12 rows containing missing values (geom_point).
plot k (stand age at half biomass asymptote)
## Warning: Removed 12 rows containing missing values (geom_point).
Caclulations - weighted averages
ge (stand biomass enhancement factor in % 2000-2021)
## region weighted.ge weighted.ge.std_Error 95 % CI, upper 95 % CI, lower
## 1 entire US 0.64186955 0.08855911 0.81544540 0.46829370
## 2 pacific -0.05258158 0.02907018 0.00439597 -0.10955912
## 3 east 0.62254977 0.04104178 0.70299165 0.54210789
## 4 interior west 0.07190135 0.07289179 0.21476926 -0.07096656phi (effect of DeltaPDSI)
## region weighted.phi weighted.phi.std_Error 95 % CI, upper
## 1 entire US 0.014850562 2.965367e-08 0.014850620
## 2 pacific 0.006361287 9.794231e-04 0.008280956
## 3 east 0.004592308 1.019822e-03 0.006591159
## 4 interior west 0.003896967 9.545942e-04 0.005767971
## 95 % CI, lower
## 1 0.014850504
## 2 0.004441617
## 3 0.002593458
## 4 0.002025962alpha (biomass compensation effect)
## region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1 entire US 0.80054289 1.340699e-07 0.80054315
## 2 pacific 0.08831322 5.087893e-03 0.09828549
## 3 east 0.62745699 5.002736e-03 0.63726236
## 4 interior west 0.08477267 2.929348e-03 0.09051420
## 95 % CI, lower
## 1 0.80054263
## 2 0.07834095
## 3 0.61765163
## 4 0.07903115A (asymptote of forest biomass in Mg/ha)
## region weighted.A
## 1 entire US 444.6020
## 2 pacific 1396.6006
## 3 east 359.5654
## 4 interior west 0.0000K (stand age at half maturation in years)
## region weighted.k
## 1 entire US 339.4760
## 2 pacific 299.9999
## 3 east 372.7147
## 4 interior west 175.4720Model Bookeeping
1. Delta-B due to Delta-STDAGE
2. Delta-B due to Delta-Year (ge)
make a fig
## Warning: Removed 16224 rows containing missing values (geom_point).
3. stand age densities
make a fig
## Warning: package 'ggridges' was built under R version 4.2.2## Picking joint bandwidth of 7.36
